Blender installation package not opening
Check the version you are downloading. And if the executable didn't work you can try downloading the zip package where you do not need to do any installation. The zip package lets you drag it's content into any directory and run blender directly from it.

A Zip package can be found just below the installer versions.

But you may have to do a manual registry entry using this method. That being said 2.7 versions have a registry bug that sometimes doesn't register even if you do a proper install so this step may still be necessary even if you did a proper windows installation.